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Publisher: Springer | Pages: 284 | 2009 | ISBN 0387096094 | PDF
Marginal Models for Dependent, Clustered, and Longitudinal Categorical Data provides a comprehensive overview of the basic principles of marginal modeling and offers a wide range of possible applications. Marginal models are often the best choice for answering important research questions when dependent observations are involved, as the many real world examples in this book show.
In the social, behavioral, educational, economic, and biomedical sciences, data are often collected in ways that introduce dependencies in the observations to be compared. For example, the same respondents are interviewed at several occasions, several members of networks or groups are interviewed within the same survey, or, within families, both children and parents are investigated. Statistical methods that take the dependencies in the data into account must then be used, e.g., when observations at time one and time two are compared in longitudinal studies. At present, researchers almost automatically turn to multi-level models or to GEE estimation to deal with these dependencies. Despite the enormous potential and applicability of these recent developments, they require restrictive assumptions on the nature of the dependencies in the data. The marginal models of this book provide another way of dealing with these dependencies, without the need for such assumptions, and can be used to answer research questions directly at the intended marginal level.
Table of contents
1. Introduction
2. Loglinear marginal models
3. Nonloglinear marginal models
4. Marginal analysis of longitudinal data
5. Causal analysis: structural equation models and (quasi) experimental designs
6. Marginal modeling with latent variables
7. Conclusions, extensions, applications
Marginal Models: For Dependent, Clustered, and Longitudinal Categorical Data
In the first chapter, we will explain the basic concepts of marginal modeling.
Because loglinear models form the basic tools of categorical data analysis, loglinear
marginal models will be discussed in Chapter 2. However, not all interesting research
questions involving marginal modeling can be answered within the loglinear framework.
Therefore, in Chapter 3 it will be shown how to estimate and test nonloglinear
marginal models. The methods explained in Chapters 2 and 3 will then be applied
in Chapter 4 to investigate changes over time using longitudinal data. Data resulting
from repeated measurements on the same subjects probably form the most important
field for the application of marginal models. In Chapter 5, marginal modeling
is related to causal modeling. For many decades now, Structural Equation Modeling
(SEM) has formed an important and standard part of the researcher’s tool kit,
and it has also been well developed for categorical data. It is shown in Chapter 5
that there are many useful connections between SEM and marginal modeling for the
analysis of cross-sectional or longitudinal data. The use of marginal models for the
analysis of (quasi-)experimental data is another important topic in Chapter 5. In all
analyses in Chapters 2 through 5, the observed data are treated as given, in the sense
that no questions are asked regarding their reliability and validity. All the analyses
are manifest-level analyses only. Marginal models involving latent variables are the
topic of Chapter 6. In the final Chapter 7, a number of important conclusions, discussions
and extensionswill be discussed: marginal models for continuous data, alternative
estimation methods, comparisons of marginal models to random and fixed-effect
models, some specific applications, possible future developments, and very importantly,
software and the contents of the book’s website.
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